I don't shoot coyotes often while hunting other things, but if I were to do it with a turkey load past 20 yards I think I would aim double-lung broadside. He'll likely run off, but put 500 tungsten pellets into his chest cavity and he'll tip over dead pretty quick.
I say this because I've shot one in the head with a shotgun and left him there for an hour or two thinking he was dead only to walk up on him and realize he was paralyzed, slowly dying, and gasping air. I'm happy to kill one, but nobody wants to do it like that. Unless I'm shooting a load tailored for breaking coyote sized skulls, I'm shoot for the ribcage. And I'd watch him run off, and be perfectly confident that he'll tip over dead in a few seconds.